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BUREAU OF MINES V/t / 
INFORMATION CIRCULAR/1990 



Baseline Tensile Testing at the Wire 
Rope Research Laboratory 



By William M. McKewan and Anthony J. Miscoe 




(801 

\ YEARS g 

%U OF ^ 



U.S. BUREAU OF MINES 
1910-1990 

THE MINERALS SOURCE 



Mission: As the Nation's principal conservation 
agency, the Department of the Interior has respon- 
sibility for most of our nationally-owned public 
lands and natural and cultural resources. This 
includes fostering wise use of our land and water 
resources, protecting our fish and wildlife, pre- 
serving the environmental and cultural values of 
our national parks and historical places, and pro- 
viding for the enjoyment of life through outdoor 
recreation. The Department assesses our energy 
and mineral resources and works to assure that 
their development is in the best interests of all 
our people. The Department also promotes the 
goals of the Take Pride in America campaign by 
encouraging stewardshipandcitizen responsibil- 
ity for the public lands and promoting citizen par- 
ticipation in their care. The Department also has 
a major responsibility for American Indian reser- 
vation communities and for people who live in 
Island Territories under U.S. Administration. 



Information Circular 9255 

M 



Baseline Tensile Testing at the Wire 
Rope Research Laboratory 

By William M. McKewan and Anthony J. Miscoe 



UNITED STATES DEPARTMENT OF THE INTERIOR 
Manuel Lujan, Jr., Secretary 

BUREAU OF MINES 
T S Ary, Director 







Library of Congress Cataloging in Publication Data: 



McKewan, William M. 

Baseline tensile testing at the Wire Rope Research Laboratory / by William M. 
McKewan and Anthony J. Miscoe. 

p. cm. - (Information circular / Bureau of Mines; 9255) 

Includes bibliographical references p. 23. 

Supt. of Docs, no.: 128.27:9255. 

1. Mine hoisting-Equipment and supplies-Testing. 2. Wire rope-Fatigue- 
Testing. 3. Fatigue testing machines. I. Miscoe, Anthony J. II. Title. III. Series: 
Information circular (United States. Bureau of Mines); 9255. 

TN295.U4 [TN339] 622 s-dc20 [622'.6] 89-600355 CIP 



CONTENTS 



Page 



Abstract 1 

Introduction 2 

Equipment description 2 

Experimental design 4 

Experimental procedure 5 

Experimental results 5 

Typical results 5 

Summary of normal breaks 7 

Construction stretch 12 

Breaking load versus gauge length 13 

Breaking load versus reel position 13 

Effects of stroke rate on results 15 

Effect of gauge length on modulus of elasticity 15 

Comparison of zinc and epoxy socketing 21 

Torque calculations 22 

Summary 23 

References 23 

ILLUSTRATIONS 

1. Tensile and axial fatigue testing machine 3 

2. Typical test data, rope D 8 

3. Typical test data, rope B 9 

4. Stress versus strain, rope B 13 

5. Effect of prestretching on rope samples, rope B 13 

6. Breaking load versus sample length 14 

7. Effect of sample position on reel 15 

8. Effect of log stroke rate, rope G 15 

9. Modulus versus gauge length for various ropes 16 

10. Elongation versus gauge length at 100,000-psi stress for various ropes 20 

11. Elongation correction for stretch of socket filler versus load 21 

12. Breaking strength and elongation versus gauge length for epoxy and zinc terminations 21 

13. Modulus versus gauge length for epoxy and zinc terminations 22 

TABLES 

1. Tensile and axial fatigue testing machine specifications 3 

2. Characteristics of wire ropes used in tests 4 

3. Typical baseline test on wire rope D 6 

4. Typical baseline test on wire rope B 7 

5. Summary of test series on rope A 10 

6. Summary of test series on rope B 10 

7. Summary of test series on rope C 10 

8. Summary of test series on rope D 11 

9. Summary of test series on rope E 11 

10. Summary of test series on rope F 11 

11. Effect of stroke rate, rope G test series 12 

12. Test series on zinc-filled sockets, rope H 12 

13. Baseline tensile test summary 12 

14. Effect of sample length on modulus and elongation at 100,000-psi stress for rope A 17 

15. Effect of sample length on modulus and elongation at 100,000-psi stress for rope B 18 

16. Effect of sample length on modulus and elongation at 100,000-psi stress for rope C 18 

17. Effect of sample length on modulus and elongation at 100,000-psi stress for rope D 18 

18. Effect of sample length on modulus and elongation at 100,000-psi stress for rope E 18 

19. Effect of sample length on modulus and elongation at 100,000-psi stress for rope F 19 

20. Effect of sample length on modulus and elongation at 100,000-psi stress for rope H 19 



TABLES - Continued 



Page 



21. Elongation correction versus rope diameter at 100,000-psi stress 

22. Calculation of Gibson's torque constant 



21 

23 





UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT 


ft 


foot 


lbf-ft/kip 


pound (force) foot per kip 


ft/min 


foot per minute 


m 


meter 


gpm 


gallon per minute 


min 


minute 


hp 


horsepower 


mm 


millimeter 


in 


inch 


pet 


percent 


in/min 


inch per minute 


pet in/in 


percent inch per inch 


kip/in 2 


kip per square inch 


psi 


pound (force) per square inch 


lb 


pound 


s 


second 


lbf-ft 


pound (force) foot 







BASELINE TENSILE TESTING AT THE WIRE ROPE LABORATORY 

By William M. McKewan 1 and Anthony J. Miscoe 2 



ABSTRACT 

The U.S. Bureau of Mines has established a wire rope research laboratory to examine the factors 
that affect the life of wire rope. Ropes of sizes ranging from 3/4 to 2 in. in diameter and from 2 to 35 ft 
in length were tested to determine their breaking strength, elongation, and torque. This was done to 
characterize the test equipment on ropes used in mine hoisting systems. 



Metallurgist. 

Supervisory physical scientist. 
Pittsburgh Research Center, U.S. Bureau of Mines, Pittsburgh, PA. 



INTRODUCTION 



The U.S. Bureau of Mines hoisting systems develop- 
ment project is an effort to improve the safety and 
efficiency of mine hoisting systems. A major part of this 
effort involves the study of the degradation of wire rope 
during its service life. Some 500 hoists are used in the 
United States, and in most of them, the cages for 
personnel and the skips for product are raised and lowered 
by a single wire rope. Cages may hold as many as 
100 people, and shafts are as deep as 7,000 ft. 

Skips have fallen in this country, with accidents to 
nearby personnel and damage to the hoisting system. The 
accidents resulting from retrieving the rope, repairing, and 
putting the shaft back into service are significant. No 
cages have fallen in the United States, but the probability 
of such occurrences will escalate in the future because 
mining deeper reserves will require longer ropes and 
higher hoisting speeds. Lower safety factors will be used 
since regulations state that the safety factor can be reduced 
from 7 to 4 as shaft depth increases from to 4,000 ft and 
more. The fact that cages have fallen in foreign countries 
confirms that this research is not only desirable but 
necessary. 

While the technology of fabricating wire ropes has 
achieved a high degree of sophistication, the quantitative 
understanding of the degradation of the rope during 
service is at a very low level. A wire rope is really a 
mechanical system having a very complex geometry. It is 
actually a multilayer spring with internal damping. When 
a loaded wire rope is bent around a sheave to change its 
direction, the mechanics become even more complicated 
since transverse forces are introduced. In addition to the 
internal wear caused by the wires sliding on each other, 
external wear is caused by rubbing and sliding in the 
sheave. Adding to the problem are the dynamics of ropes 
up to a mile long and ropes traveling at speeds up to 
2,850 ft/min, accelerating and decelerating with attached 
loads on imperfectly aligned guides. Also to be considered 
are the mine shaft environmental conditions of abrasive 
dirt and acid or alkaline moisture. Consequently, mine- 
hoist ropes endure great punishment. Analysis of the 



effects of these factors on the deterioration of a wire rope 
therefore requires an extensive research program and data 
generation with high precision. 

The Wire Rope Research Laboratory (WRRL) was es- 
tablished by the Bureau to examine the factors that affect 
wire rope strength, and ultimately, its useful life. At 
present, hoist ropes in mines are inspected both visually 
and by nondestructive sensors. A judgment is made, based 
on the observations and experience of the observer, as 
to whether the rope meets the retirement criteria of the 
U.S. Mine Safety and Health Administration (MSHA) (if 
and should be retired from service. At some mines, ropes 
are retired after a certain period of time has occurred or 
a given amount of tonnage has been lifted. The purpose 
of the WRRL is to provide accurate data to determine the 
effects of variables on the reduction of the strength of wire 
rope during its service life so that judgment becomes less 
of a factor. 

The best way to measure the deterioration of strength 
in a wire rope is to measure its ultimate or breaking 
strength, but this obviously cannot be done while the rope 
is in service. At the WRRL, ropes will be deteriorated by 
a bending fatigue machine of unique design, containing 
three sheaves that will exercise a 1,000-ft length of rope to 
produce nine different levels of fatigue at a predetermined 
tensile load and travel speed. Visual inspection and non- 
destructive testing (NDT) profiles will be made periodi- 
cally as the rope is cycled. After some time, broken wires 
and other indications of wear will determine that the rope 
be removed. Sections of special interest will be cut out, 
then further subdivided for detailed examination. The ex- 
amination will consist of four analyses (in addition to the 
NDT profile): wire-by- wire examination for correlation 
with the NDT profiles, single-wire torsion tests, metallo- 
graphic examination, and tensile strength measurements. 

The primary objectives of the baseline testing program 
covered in this report were to determine (1) the operating 
characteristics of the tensile machine, (2) the precision of 
data produced by the tensile machine, and (3) the proper- 
ties of the wire rope samples used during tensile testing. 



EQUIPMENT DESCRIPTION 



Although the tensile machine was designed primarily 
for tensile strength tests on wire rope specimens in support 
of bending fatigue research, it also has the versatility to 
test fatigue under cyclic axial force. The main application 
of this tensile machine will be to measure breaking 
strengths, elongations, and torques of new ropes for 
comparison with measurements made after the ropes have 
been degraded on the bending fatigue machine. These 
measurements will provide quantitative data to establish 



the effects of service conditions on the life of wire ropes. 
New and used ropes from mine hoists, obtained through 
cooperative agreements with mining companies, will also 
be tested to assess the effects of real-life use. The ma- 
chine is shown in figure 1. System specifications are listed 
in table 1. 

Italic numbers in parentheses refer to items in the list of references 
at the end of this report. 



'///////""""■ 




Figure 1. -Tensile and axial fatigue testing machine. 



Table 1, -Tensile and axial fatigue testing 
machine specifications 

Description Specification 

Maximum rope tension lb . . 800.000 

Maximum rope diameter in . . 2-1/2 

Specimen length ft . . 2-33 

Maximum actuator speed in/min . . 16 

Hydraulic system: 

Row rate gpm . . 70 

Pressure psi . . 3.000 

Drive motor hp . . 125 

The machine is essentially a hydraulically actuated ten- 
sile testing machine in a horizontal position rather than 
the usual vertical position to reduce vertical height re- 
quirements and for ease of access. It is composed of three 
elements operating in conjunction: the load frame, the 
electrical console, and hydraulic power supply. The load 
frame contains the hvdraulic crosshead locks. The locks 



sustain full rated load in either direction with zero slippage 
and zero backlash. Safety containers for the specimen are 
provided for operator protection during testing. 

Functionally, the test machine is a closed-loop servohy- 
draulic system in which high-pressure hydraulic fluid under 
the precise control of a servovalve is provided to the hy- 
draulic actuator, which applies the load to the specimen. 
To accomplish this, the system controller accepts externally 
generated electrical control and feedback signals from the 
transducer. These signals are compared to detect any 
error, and the resulting signal is used to control the servo- 
valve. Several operating variables can be selected as con- 
trol parameters by choosing the appropriate transducer 
for the feedback signal. The controllable parameters are 
displacement of the actuator, load applied to the specimen, 
and torque generated by the wire rope specimen as an ax- 
ial load is applied. 



The electronic control console contains all the necessary 
components for servocontrol, hydraulic power control, sig- 
nal conditioning, test parameter readout, and interlock 
functions. It also contains a digital computer and the nec- 
essary interfaces to record, manipulate, and plot the testing 
data. 

The factors examined in the baseline series were 

1. The precision of the data generated by the system 
for ultimate strength, elongation, and torque. 



2. The effectiveness of resin sockets to withstand rope 
ultimate-strength loads and comparison of resin sockets 
with zinc (spelter) sockets. 

3. The effect of actuator speed on generated data. 

4. The effect of sample length on generated data. 

5. Variation of generated data along the length on a 
single reel of rope. 



EXPERIMENTAL DESIGN 



There are a number of factors that can be determined 
during the tensile testing of wire rope. Some are measured 
directly, such as breaking load, and some are calculated, 
such as modulus of elasticity. Before a test is conducted, 
certain physical measurements are made on the rope. 
These are (1) gauge length, the rope length between the 
sockets, (2) rope diameter, and (3) lay length. From the 
diameter and the rope construction, the metallic area can 
be calculated. 

During the course of the program the operational char- 
acteristics of the machine were determined. The measure- 
ments made during testing were (1) the displacement of 
the actuator rod, or the stroke, (2) the load applied to the 
specimen, and (3) the torque generated by the specimen as 
an axial load is applied. The sensors for these measure- 
ments were calibrated by the machine manufacturer. 

Bureau researchers wanted to gain as much information 
as possible from the testing, both about the tensile 
machine and about the different samples of rope. It was 
known in advance that the manufacturer's catalog does 



not provide any detailed information about a rope. 
Manufacturers are required only to meet a minimum 
strength, nothing else; they are not required to give data 
on the actual breaking strength, the elongation, the 
chemical composition, or the microscopic structure of the 
rope. Therefore, the experimental work was designed to 
gain maximum data from as few tests as possible. 

Originally, 10 tests were scheduled for each rope series. 
The characteristics of the ropes chosen for each series are 
shown in table 2. Samples were cut to the following 
lengths: 5, 10, 15, 20, and 35 ft. Two samples were taken 
of each. The 10 samples were cut from the reel in random 
order. From a procedure of this nature, the precision of 
the testing could be calculated. In addition, the effects of 
sample size on the results and the uniformity of the rope 
on the reel could be determined. Later, it was decided to 
add 2-ft samples to the test program to increase the range 
of the data and to substitute 30-ft samples for the 35-ft 
samples to allow for the larger elongations. 



Table 2.-Characteristics of wire ropes used in tests 



Rope 



(All ropes were fiber core, improved plow steel, set in socket with epoxy resin, 
and tested at 1-in/min stroke rate, unless otherwise noted) 



Diam, 
in 



Description 



Strength, 1 


Samples 


kips 


tested 


83.6 


10 


184.0 


12 


129.2 


10 


47.6 


10 


310.0 


11 


320.0 


13 


129.2 


9 


184.0 


5 



1 

1-1/2 
1-1/4 
3/4 
1-7/8 
2 

1-1/4 
1-1/2 



6 x 25 filler wire, 6-in right regular lay ... . 

6x19 Seale, 10-in right Lang lay 

6 x 25 filler wire, 8-in right Lang lay 

6x19 Seale, 5.25-in right Lang lay 

6 x 25 filler wire, 12.75-in right Lang lay . . 
6 x 25 filler wire, 13.125-in right regular lay 
6 x 25 filler wire, 8-in right regular lay ... . 
6x19 Seale, 10-in right Lang lay 



'Catalog. 

2 Tested at stroke rates of 0.0625, 0.125, 1, 8, and 16 in/min. 

3 2nc-filled socket. 



EXPERIMENTAL PROCEDURE 



Enough rope was cut to allow for the amount that 
would be in the sockets. The ends were seized, broomed, 
and cleaned. The brooms were cleaned in a vented tank 
of trichloroethane and then washed with steam and 
detergent to remove any residual matter. The brooms 
were then closed, inserted into the sockets and set in an 
epoxy resin. With this procedure, there was no problem 
with the brooms pulling out of the sockets. After curing 
for about an hour, the samples were ready for testing. 
One series of samples was made commercially with zinc- 
filled sockets, using rope from a reel that had been 
previously tested, to compare the results obtained with zinc 
and epoxy sockets. 

The samples were placed in the tensile machine, and 
the testing was begun. Initially a prestretch load of about 
5 to 10 kips was placed on the rope, and the stroke was set 
at zero. This procedure led to an S-shaped curve during 
the elastic portion of the test, because of the construction 
stretch that exists in new rope. During the second series 
of samples, a prestretch load equal to 20 pet of the 
breaking strength was placed on the sample for 10 min or 
until the rope stopped elongating. This load was then 
removed, and the test was conducted as before. This pro- 
cedure eliminated construction stretch and the S-shaped 
curves. The 20-pct prestretch load was used for all of the 
remaining tests. Construction stretch and the S-curves are 
discussed later in this report. 

The following measurements were made during the 
testing as a function of time: (1) load in kips, (2) stroke 



in inches, (3) torque in kip-inches. From these measure- 
ments the other factors can be calculated, such as stress, 
strain, and elongation. 

The "Wire Rope Users Manual" (2) gives certain speci- 
fications for determining breaking strengths of wire ropes: 

The breaking strength is the ultimate load 
registered on a wire rope sample during a tension 
test.... All discussion of strength is predicated on 
the assumption of there being a gradually applied 
load that will not exceed one inch per minute.... A 
minimum acceptance strength, 2-1/2% lower than 
the published nominal breaking strengths, was 
established as the industry tolerance.... The sample's 
length must not be less than 3 ft (0.91 m) between 
sockets for ropes with diameters of from 1/8 inch 
(3.2 mm) through 3 inches (77 mm); on ropes with 
larger (over 3 inches) diameters, the clear length 
must be a least 20 times the rope diameter. The test 
is considered valid only if failure occurs 2 inches 
(51 mm) or more from either of the sockets, or from 
the holding mechanism. 

The "Wire Rope Users Manual" specifications were fol- 
lowed for most of the testing. The exceptions were (1) a 
few 2-ft samples were tested to aid in the determination 
of modulus of elasticity, and (2) a series of tests were run 
over a range of stroke rates to determine the effect of this 
variable. 



EXPERIMENTAL RESULTS 



TYPICAL RESULTS 

There were eight series of rope samples run during 
the baseline testing. Of these samples, only the 80 samples 
that broke more than the standard two in from the sockets 
were used for the determination of breaking strength. 
However, samples that broke near the sockets could be 
used for calculation of modulus of elasticity and yield 
because these data are accumulated prior to the breaking 
point and are independent of behavior in the plastic region 
near the breaking point. 

The data from two tests are shown in tables 3 and 4. 
The stroke in inches is shown to be a function of time in 
seconds since the stroke was set at 1 in/min. This can be 
seen easily by comparing the stroke data with the time at 
60-s intervals. The load in kips and the torque in kip- 
inches were measured by the machine at the designated 
time intervals. The torque in pound (force) feet was 



calculated from the torque in kip-inches. The elongation 
in inches was determined from the stroke, using a com- 
pliance factor determined by the machine configuration 
and the socket diameter. This factor multiplied by the 
load is subtracted from the stroke to give the elongation. 
The compliance factor takes care of any tension or 
compression in the machine parts, the grips, and the 
sockets. This is a significant correction as can be seen by 
comparing stroke with elongation. The stress in kips per 
square inch is calculated by dividing the load by the rope 
metallic area. The strain in percent inch per inch is 
calculated by dividing the elongation by the rope gauge 
length in inches and multiplying by 100. 

From the data in tables 3 and 4, the curves in fig- 
ures 2 and 3, respectively, were plotted. From every run 
made during the baseline testing, a table was generated 
and three curves were plotted. 



Table 3.-Typical baseline test on wire rope D 



Time, s 



Stress. 
kip/in 



Strain, 
pet in/in 



Torque, 
Ibf-ft 



Load, 
kips 



Elongation, 
in 



Stroke, 
in 



1.5 . . 
12.0 . 
24.0 . 
36.0 . 
48.0 . 

60.0 . 
72.0 . 
84.0 . 
96.0 . 
108.0 

120.0 
132.0 
144.0 
156.0 
168.0 

180.0 
192.0 
204.0 
216.0 
228.0 

240.0 
252.0 
264.0 
276.0 
288.0 

300.0 
312.0 
324.0 
325.5 
327.0 



13.490 


0.021 


24.2 


2.992 


0.025 


0.027 


26.100 


.167 


47.6 


5.789 


.198 


.203 


44.382 


.333 


83.4 


9.844 


.397 


.405 


63.981 


.497 


121.1 


14.191 


.592 


.603 


82.926 


.658 


156.0 


18.393 


.784 


.799 


102.858 


.826 


194.4 


22.814 


.984 


1.002 


122.624 


.990 


229.3 


27.198 


1.179 


1.201 


140.906 


1.154 


262.3 


31.253 


1.374 


1.399 


157.534 


1.317 


293.3 


34.941 


1.568 


1.596 


171.740 


1.480 


319.6 


38.092 


1.763 


1.793 


183.693 


1.651 


340.9 


40.743 


1.967 


1.999 


193.602 


1.817 


358.3 


42.941 


2.164 


2.198 


201.533 


1.982 


372.5 


44.700 


2.361 


2.396 


208.030 


2.146 


385.0 


46.141 


2.556 


2.593 


213.206 


2.313 


391.6 


47.289 


2.756 


2.793 


217.556 


2.481 


399.3 


48.254 


2.956 


2.994 


220.694 


2.646 


402.8 


48.950 


3.152 


3.191 


223.665 


2.815 


407.6 


49.609 


3.354 


3.393 


226.032 


2.979 


409.7 


50.134 


3.549 


3.589 


227.687 


3.145 


411.9 


50.501 


3.747 


3.787 


229.504 


3.313 


414.8 


50.904 


3.947 


3.987 


230.771 


3.482 


417.5 


51.185 


4.147 


4.188 


232.146 


3.651 


416.3 


51.490 


4.349 


4.390 


232.809 


3.814 


416.3 


51.637 


4.543 


4.584 


233.855 


3.983 


416.0 


51.869 


4.745 


4.786 


234.238 


4.148 


415.0 


51.954 


4.941 


4.982 


234.842 


4.319 


415.8 


52.088 


5.145 


5.186 


235.063 


4.483 


413.8 


52.137 


5.341 


5.382 


235.176 


4.507 


413.8 


52.162 


5.369 


5.410 


235.063 


4.527 


414.0 


52.137 


5.393 


5.434 



From the plots of load versus elongation on fig- 
ures 24 and 3/4 and the data from the tables, the breaking 
strength and the breaking elongation can be determined. 
The breaking strength is defined as the maximum load that 
the rope attains. The breaking elongation is defined as the 
maximum elongation that the rope attains, which occurs 
when the rope breaks. The maximum load does not nec- 
essarily occur at the maximum elongation, as is shown in 
table 3. 

Figures 25 and 35 show plots of stress versus strain. 
The elastic region is the initial straight-line portion of the 
plot where stress is proportional to strain. The plastic 
region is the final part of the plot where the stress is no 
longer proportional to strain. The slope of the straight- 
line portion of a stress-strain curve is defined as the 



modulus of elasticity. It is equal to the stress divided by 
the strain and is in units of pounds per square inch. 
Because the stress-strain plots for many metals and for 
wire rope do not show a well-defined transition from 
elastic to plastic behavior, it is customary to define the 
yield stress by drawing a line parallel to the slope of the 
stress-strain plot and displaced 0.2 pet of the gauge length 
to the right. This line will intersect the curve in the plastic 
region. This point of intersection is defined as the yield 
stress. The strain at that point is the yield strain. 

Figures 2C and 3C show plots of torque versus load. 
As can be seen from the figures, torque is proportional to 
load almost to fracture. The slope of the torque-versus- 
load plot is called the Torque K. It has the units of pound 
(force) feet per kip. 



Table 4.-Typical baseline test on wire rope B 



Time, s 



Stress. 
kip/in 



Strain, 
pet in/in 



Torque, 
Ibf-ft 



Load, 
kips 



Elongation, 
in 



Stroke, 
in 



1.5 .. 
6.0 .. 
12.0 . 
18.0 . 
24.0 . 

30.0 . 

36.0 . 

42.0 . 

48.0 . 

54.0 . 

60.0 . 

66.0 . 

72.0 . 

78.0 . 

84.0 . 

90.0 . 
96.0 . 
102.0 
108.0 
114.0 

120.0 
126.0 
132.0 
138.0 
144.0 

150.0 
156.0 
162.0 
168.0 
174.0 

180.0 
186.0 
192.0 
198.0 
204.0 
207.0 



13.051 


0.041 


188.3 


11.578 


0.024 


0.031 


25.607 


.158 


386.8 


22.716 


.092 


.106 


42.293 


.315 


647.6 


37.518 


.182 


.206 


55.289 


.475 


839.7 


49.047 


.275 


.306 


68.781 


.635 


1,045.8 


61.016 


.367 


.406 


83.099 


.793 


1,254.4 


73.718 


.459 


.506 


98.188 


.946 


1,478.3 


87.103 


.548 


.603 


112.892 


1.108 


1,694.6 


100.147 


.641 


.705 


126.713 


1.262 


1,895.6 


112.408 


.731 


.802 


139.875 


1.421 


2,088.9 


124.084 


.822 


.901 


152.155 


1.588 


2,267.0 


134.978 


.919 


1.005 


162.838 


1.751 


2,418.4 


144.455 


1.013 


1.105 


173.026 


1.914 


2,564.8 


153.493 


1.108 


1.205 


181.892 


2.078 


2,691.9 


161.358 


1.203 


1.305 


189.823 


2.236 


2,795.0 


168.393 


1.294 


1.401 


196.596 


2.407 


2,891.7 


174.402 


1.393 


1.504 


202.708 


2.574 


2,973.1 


179.824 


1.490 


1.604 


207.885 


2.737 


3,036.8 


184.416 


1.584 


1.701 


212.621 


2.908 


3,100.3 


188.618 


1.683 


1.803 


216.476 


3.074 


3,143.6 


192.037 


1.779 


1.901 


219.724 


3.240 


3,183.0 


194.919 


1.875 


1.999 


222.809 


3.415 


3,218.7 


197.655 


1.976 


2.102 


225.397 


3.587 


3,242.8 


199.951 


2.076 


2.203 


227.655 


3.752 


3,261.9 


201.954 


2.172 


2.300 


229.472 


3.922 


3,278.4 


203.566 


2.270 


2.399 


231.124 


4.096 


3,289.9 


205.032 


2.371 


2.501 


232.390 


4.271 


3,298.8 


206.155 


2.472 


2.603 


233.657 


4.443 


3,307.7 


207.279 


2.571 


2.703 


234.703 


4.615 


3,309.0 


208.207 


2.671 


2.803 


235.364 


4.780 


3,305.2 


208.793 


2.766 


2.899 


236.026 


4.952 


3,302.6 


209.380 


2.866 


2.999 


236.686 


5.124 


3,303.8 


209.966 


2.966 


3.099 


236.961 


5.298 


3,296.3 


210.210 


3.067 


3.200 


237.457 


5.469 


3,292.4 


210.650 


3.165 


3.299 


237.457 


5.640 


3,281.0 


210.650 


3.264 


3.398 


237.732 


5.726 


3,277.2 


210.894 


3.314 


3.448 



SUMMARY OF NORMAL BREAKS 

A normal break is defined as a break that occurs 2 in 
or more from the socket. Only data obtained with normal 
breaks were accepted for the measurement of breaking 
strength. The summaries of data for the eight series of 
rope tests are shown in tables 5 to 12. Also shown in the 
summary tables are the means, the standard deviations, 
and the percentage that the standard deviations are of the 
means. In table 13 the means, standard deviations, and 



the percent standard deviations of all of the ropes are 
shown for the breaking strength (load), the modulus of 
elasticity, the breaking stress, the yield stress, and the 
torque constant. It is apparent from examining the 
percent standard deviation columns that the precision is 
good for the measurement of load and torque. It is also 
apparent that any measurement involving elongation, such 
as modulus of elasticity, has poor precision, considering all 
of the data from a series. The measurement of stroke, 
elongation, and modulus of elasticity are discussed later. 



240 




7 ° D 
/ □ 



D D 



D D 



D D D n 1 o o id 



/ Yield, 191.9 kip/in 

Breaking stress, 2351 kip/in 2 
/ Modulus, 11.41 * I0 6 psi 



2 3 4 5 

ELONGATION, in 



KEY 

Y = 114.054827* X+ 8.310668 

0.2-pct yield 



2 3 

STRAIN, pet in/in 




20 30 40 

LOAD, kips 



50 60 



Figure 2.-Typical test data, rope D. 



240 



200 



240 




160- 



120 



0.5 



I dD dDooiddouj 



1.0 1.5 2.0 2.5 

ELONGATION, in 



3.0 3.5 



Yield, 182.3 kip/in* 
Breaking stress, 2377 kip/ in 2 
Modulus, 8.90 « I0 6 ps. 

KEY 
•Y = 89.04544*X + 13.00276 



0.2-pct yield 



2 3 4 

STRAIN, pet in/in 




100 150 

LOAD, kips 



250 



Figure 3.-Typical test data, rope B. 



10 



Table 5.-Summary of test series on rope A 



Sample 
length, 
ft 

5.01 

5.07 

10.00 

10.13 

14.96 

15.21 

20.03 

20.27 

35.21 

35.32 

Mean .... 

SD 



Modulus of 

elasticity, 

10 6 psi 



Break 



Yield 



Load, 


Elonga- 


Stress, 


Strain, 


Stress, 
kip/in 


Strain, 


kips 


tion, in 


kip/in 2 


pet in/in 


pet in/in 


92.06 


2.78 


228.00 


4.62 


188.00 


2.41 


92.38 


2.61 


228.80 


4.28 


183.70 


2.03 


92.04 


5.04 


288.00 


4.20 


183.90 


2.03 


91.09 


5.07 


225.60 


4.18 


191.90 


2.44 


89.50 


6.84 


221.70 


3.81 


185.20 


2.30 


91.09 


7.76 


225.60 


4.21 


186.90 


2.27 


91.16 


9.82 


225.80 


4.09 


182.30 


1.93 


91.04 


9.76 


225.50 


4.01 


187.30 


2.19 


90.06 


16.48 


223.10 


3.90 


185.50 


2.14 


90.96 


16.93 


225.30 


3.99 


183.90 


1.96 


91.14 


NAp 


225.74 


4.13 


185.86 


2.17 


.89 


NAp 


2.19 


.23 


2.78 


.18 



Torque K, 
Ibf-ft/kip 



Reel 

position, 

ft 



8.48 
9.29 
9.50 
8.89 
9.43 
9.49 
9.77 
9.59 
9.87 
9.90 
9.42 
.44 



7.69 
8.14 
8.26 
8.22 
7.92 
8.23 
8.46 
8.47 
8.26 
8.34 
8.20 
.24 



2.9 

251.0 

116.8 

226.5 

13.7 

240.0 

264.4 

132.7 

203.0 

39.7 

NAp 

NAp 



SD . . pet 



4.72 



0.97 



NAp 



0.97 



5.52 



1.50 



8.41 



2.91 



NAp 



NAp Not applicable. 



SD Standard deviation. 



Table 6.-Summary of test series on rope B 



Sample 


Modulus of 

elasticity, 

10 6 psi 




Break 




Yield 


Torque K, 
Ibf-ft/kip 


Reel 


length, 
ft 


Load, 
kips 


Elonga- Stress, 
tion, in kip/in 2 


Strain, 
pet in/in 


Stress. Strain, 
kip/in pet in/in 


position, 
ft 



4.81 . . 

4.82 . . 
4.82 . . 
5.06 . . 
9.64 . . 
10.02 . 
14.64 . 
14.71 . 
19.60 . 
20.17 . 
34.88 . 
35.00 . 

Mean 
SD.. 



7.84 

8.90 

8.63 

8.11 

10.51 

10.35 

10.95 

11.00 

11.04 

11.33 

11.76 

12.07 

10.21 

1.46 



210.60 
210.90 
210.60 
207.80 
207.80 
209.10 
208.20 
207.70 
207.70 
208.20 
207.40 
207.70 
208.64 
1.31 



3.68 

3.31 

3.42 

3.34 

5.49 

6.76 

9.93 

8.74 

12.56 

12.00 

19.06 

19.49 

NAp 

NAp 



237.30 
237.70 
237.30 
234.30 
234.30 
235.70 
234.70 
234.20 
234.10 
234.70 
233.80 
234.20 
235.19 
1.43 



6.37 
2.28 
5.91 
5.50 
4.75 
5.62 
5.66 
4.95 
5.34 
4.96 
4.55 
4.63 
5.04 
1.03 



188.30 
182.30 
185.30 
185.10 
185.70 
184.70 
182.00 
185.30 
183.10 
185.10 
182.90 
183.50 
184.44 
1.77 



2.85 
2.10 
2.22 
2.79 
2.20 
2.24 
2.06 
2.10 
2.06 
2.06 
1.69 
1.74 
2.18 
.35 



16.27 
16.28 
16.28 
16.31 
16.61 
16.39 
16.52 
16.54 
16.56 
16.53 
16.60 
16.46 
16.45 
.13 



54.58 
244.54 
250.37 
154.56 
183.72 

98.74 
212.88 

43.75 
231.21 
167.89 
231.21 

17.92 
NAp 
NAp 



SD . . pet 



14.27 



0.63 



NAp 



0.61 



20.43 



0.96 



15.90 



0.81 



NAp 



NAp Not applicable. 



SD Standard deviation. 



Table 7.-Summary of test series on rope C 



4.76 . . 

4.98 . . 

9.69 . . 

9.98 . . 

14.90 . 

14.98 . 

19.80 . 

19.94 . 

35.36 . 

35.39 . 
Mean 
SD.. 



Sample 


Modulus of 

elasticity, 

10 6 psi 




Break 




Yield 


Torque K, 
Ibf-ft/kip 


Reel 


length, 
ft 


Load, 
kips 


Elonga- Stress, 
tion, in kip/in 2 


Strain, 
pet in/in 


Stress. Strain, 
kip/in pet in/in 


position, 
ft 



9.34 
9.65 
10.70 
10.94 
12.71 
11.74 
11.97 
11.02 
12.49 
12.48 
11.30 
1.18 



160.38 
159.65 
158.79 
158.33 
158.45 
158.48 
158.09 
158.38 
157.45 
157.74 
158.57 
.87 



2.69 
2.76 
4.46 
4.56 
6.75 
6.39 
8.79 
9.39 
15.39 
15.79 
NAp 
NAp 



254.30 
253.10 
251 .70 
251.00 
251.20 
251.24 
250.60 
251.10 
249.60 
250.10 
251.39 
1.39 



4.72 
4.61 
3.84 
3.86 
3.78 
3.55 
3.70 
4.09 
3.63 
3.72 
3.95 
.40 



212.60 
207.90 
214.20 
213.60 
210.40 
211.90 
211.40 
214.20 
209.50 
209.50 
211.52 
2.17 



2.32 
2.23 
2.09 
2.05 
1.74 
1.93 
1.88 
2.04 
1.80 
1.79 
1.99 
.19 



14.07 
13.92 
14.04 
14.05 
14.21 
14.35 
14.18 
14.26 
14.20 
14.11 
14.14 
.13 



101.6 

38.6 

145.6 

172.1 

158.9 

70.1 

193.6 

88.4 

334.9 

299.1 

NAp 

NAp 



SD . . pet 



10.46 



0.55 



NAp 



0.55 



10.25 



1.03 



9.74 



0.88 



NAp 



NAp Not applicable. 



SD Standard deviation. 



11 



Table 8.-Summary of test series on rope D 



Sample 


Modulus of 
elasticity, 






Break 




Yield 




Torque K, 
Ibf-ft/kip 


Reel 


length, 


Load, 


Elonga- 


Stress, 


Strain, 


Stress, 
kip/in 


Strain, 


position, 


ft 


10 6 psi 


kips 


tion, in 


kip/in 2 


pet in/in 


pet in/in 




ft 


1.88 


9.22 


52.60 


1.29 


237.20 


5.72 


184.20 


2.20 


8.16 


172.6 


4.85 


10.82 


52.37 


2.95 


236.10 


5.07 


189.30 


1.95 


8.39 


176.9 


5.09 


10.98 


52.20 


3.22 


235.30 


5.26 


186.40 


1.88 


8.25 


182.7 


9.81 


11.45 


51.66 


4.54 


232.90 


3.86 


192.60 


1.80 


8.14 


136.2 


9.93 


11.41 


52.16 


5.39 


235.20 


4.53 


191.90 


1.81 


8.16 


67.9 


15.02 


11.77 


52.17 


8.58 


235.20 


4.76 


191.60 


1.75 


8.32 


23.7 


19.96 


11.89 


52.02 


10.46 


234.50 


4.37 


192.00 


1.72 


8.28 


152.1 


20.00 


11.77 


52.21 


11.35 


235.40 


4.73 


193.60 


1.81 


8.14 


294.4 


29.93 


12.40 


51.69 


15.62 


233.00 


4.35 


188.90 


1.68 


8.40 


47.1 


30.16 


12.02 


51.83 


16.08 


233.70 


4.44 


191.60 


1.73 


8.26 


268.6 


Mean 


11.37 


52.09 


NAp 


234.85 


4.71 


190.21 


1.83 


8.25 


NAp 


SD 


.89 


.30 


NAp 


1.35 


.53 


2.99 


.IB 


.10 


NAp 


SD . . pet 


7.84 


0.57 


NAp 


0.58 


11.26 


1.57 


8.26 


1.20 


NAp 


NAp Not applicable 


SD 


Standard deviation. 















Table 9.-Summary of test series on rope E 



1.96 

2.00 

4.88 

4.91 

9.87 

9.93 

14.90 

14.97 

19.82 

20.01 

29.96 

Mean 

SD 

SD . . pet 



Sample 


Modulus of 

elasticity, 

1 6 psi 




Break 




Yield 


Torque K, 
Ibf-ft/kip 


Reel 


length, 
ft 


Load, 
kips 


Elonga- Stress, 
tion, in kip/in 2 


Strain, 
pet in/in 


Stress, Strain, 
kip/in pet in/in 


position, 
ft 



6.34 

6.83 

9.25 

9.72 

10.76 

10.49 

10.99 

11.77 

12.62 

12.34 

12.59 

10.34 

2.16 

20.93 



338.80 
338.60 
331.70 
334.00 
329.00 
330.70 
329.90 
327.60 
328.90 
326.80 
328.30 
331.30 
4.16 

1.26 



1.34 

1.42 

2.74 

2.80 

5.16 

5.08 

7.96 

7.74 

10.25 

10.10 

14.78 

NAp 

NAp 

NAp 



238.80 
238.60 
233.70 
235.30 
231.80 
233.00 
232.40 
230.80 
231.80 
230.30 
231.30 
233.44 
2.95 

1.26 



5.72 
5.92 
4.68 
4.76 
4.33 
4.29 
4.54 
4.31 
4.31 
4.21 
4.11 
4.65 
.61 

13.13 



193.30 
185.30 
181.20 
175.50 
180.40 
185.10 
179.60 
177.40 
175.50 
173.20 
177.40 
180.35 
5.76 

3.19 



2.98 
2.61 
2.10 
1.92 
1.82 
1.90 
1.81 
1.65 
1.56 
1.56 
1.58 
1.95 
.46 

23.40 



19.13 
19.53 
20.01 
19.90 
20.44 
20.30 
20.51 
20.31 
20.65 
20.71 
20.54 
20.18 
.50 

2.46 



147.5 

117.5 

3.0 

173.0 

124.5 

73.5 

108.0 

138.5 

89.5 

159.5 

21.5 

NAp 

NAp 

NAp 



NAp Not applicable. 



SD Standard deviation. 



Table 10.-Summary of test series on rope F 



Sample 


Modulus of 

elasticity, 

10 6 psi 




Break 




Yield 


Torque K, 
Ibf-ft/kip 


Reel 


length, 
ft 


Load, 
kips 


Elonga- Stress, 
tion, in kip/in 2 


Strain, 
pet in/in 


Stress, Strain, 
kip/in pet in/in 


position, 
ft 



1.94 

2.17 

2.18 

5.20 

5.38 

9.91 

10.27 

14.92 

15.34 

19.94 

20.28 

30.13 

30.23 

Mean 

SD 

SD . . pet 



5.66 

5.93 

5.17 

8.46 

9.34 

10.04 

9.15 

10.31 

10.03 

10.41 

10.52 

10.81 

11.21 

9.00 

2.08 

23.12 



352.40 
345.50 
348.90 
347.70 
347.00 
345.20 
346.70 
347.80 
348.90 
343.40 
346.30 
343.70 
344.60 
346.85 
2.53 

0.73 



1.40 

1.77 

1.96 

3.34 

3.39 

5.16 

5.94 

8.55 

8.79 

11.09 

11.19 

16.08 

16.68 

NAp 

NAp 

NAp 



218.20 
213.90 
216.10 
215.30 
214.90 
213.80 
214.70 
215.40 
216.60 
212.60 
214.40 
212.90 
213.40 
214.78 
1.57 

0.73 



6.02 
6.10 
6.79 
5.05 
4.97 
4.34 
4.82 
4.78 
4.78 
4.63 
4.60 
4.44 
4.60 
5.07 
.75 

14.77 



165.70 
167.90 
160.80 
164.20 
157.30 
162.50 
167.10 
163.20 
166.60 
164.70 
164.30 
162.90 
159.40 
163.58 
3.07 

1.88 



3.02 
2.79 
2.69 
2.10 
1.82 
1.80 
1.99 
1.80 
1.87 
1.72 
1.73 
1.66 
1.59 
2.04 
.47 

23.15 



13.73 
14.31 
13.77 
14.20 
14.35 
14.39 
14.13 
14.23 
14.01 
14.40 
14.18 
14.28 
14.47 
14.19 
.23 

1.62 



209.97 

38.25 

35.08 

42.92 

3.08 

217.07 

11.75 

230.65 

120.09 

249.24 

120.09 

162.42 

93.92 

NAp 

NAp 

NAp 



NAp Not applicable. 



SD Standard deviation. 



12 



Table 1 1 .-Effect of stroke rate, rope G test series 



Stroke, 


Sample 

length, 

ft 


Modulus of 

elasticity, 

Mpsi 




Break 




Yield 


Torque K, 


in/min 


Load, 
Kips 


Elonga- Stress, 
tion, in kip/in 


Strain, 
pet in/in 


Stress, Strain, 
kip/in pet in/in 


Ibf-ft/kip 



0.0625 

0.1250 

1.0000 

8.0000 

16.0000 

Mean 

SD 

SD pet . . 

NAp Not applicable. 



15.08 
15.05 
15.10 
15.07 
15.07 
15.07 
15.08 
15.08 
15.06 
NAp 
NAp 

NAp 



12.16 
12.17 
12.20 
12.49 
12.56 
12.57 
12.83 
13.08 
13.19 
12.58 
.38 

3.05 



137.93 
135.93 
137.96 
133.98 
136.98 
136.54 
139.38 
136.10 
137.37 
136.91 
1.53 

6.09 



4.40 
4.17 
4.32 
3.91 
4.02 
4.00 
4.13 
3.68 
3.72 
4.04 
.25 

1.12 



218.70 
215.50 
218.70 
212.40 
217.00 
216.50 
221.00 
215.80 
217.80 
217.04 
2.44 

1.12 



2.43 
2.31 
2.38 
2.16 
2.22 
2.21 
2.28 
2.03 
2.06 
2.23 
.13 

6.05 



189.60 
191.20 
191.90 
190.10 
192.80 
193.30 
195.20 
192.90 
194.30 
192.37 
1.85 

0.96 



1.67 
1.68 
1.68 
1.64 
1.64 
1.64 
1.63 
1.59 
1.58 
1.64 
.04 

2.19 



9.53 
9.56 
9.33 
9.49 
9.36 
9.58 
9.59 
9.52 
9.51 
9.50 
.09 

0.97 



SD Standard deviation. 



Table 12.-Test series on zinc-filled sockets, rope H 



5.08 

10.11 

20.12 

20.15 

30.21 

Mean 

SD 

SD . . pet 



Sample 


Modulus of 

elasticity, 

10 6 psi 




Break 




Yield 


Torque K, 
Ibf-ft/kip 


Reel 


length, 
ft 


Load, 
kips 


Elonga- Stress, 
tion, in kip/in 2 


Strain, 
pet in/in 


Stress, Strain, 
kip/in pet in/in 


position, 
ft 



8.59 
10.90 
11.30 
11.89 
12.07 
10.95 

1.40 

12.78 



210.20 
207.80 
208.10 
205.70 
206.40 
207.64 
1.74 

0.84 



3.60 

5.83 

11.92 

10.50 

17.81 

NAp 

NAp 

NAp 



237.00 
234.20 
234.60 
231.90 
232.60 
234.06 
1.98 

0.85 



5.90 
4.80 
4.94 
4.34 
4.91 
4.98 
.57 

11.43 



186.80 
183.30 
184.90 
182.60 
182.50 
184.02 
1.83 

0.99 



2.27 
1.81 
1.80 
1.66 
1.64 
1.84 
.25 

13.88 



16.42 
16.52 
16.55 
16.50 
16.73 
16.54 
.11 

0.69 



NAp 
NAp 
NAp 
NAp 
NAp 
NAp 
NAp 

NAp 



NAp Not applicable. 



SD Standard deviation. 



Table *3.-Baseline tensile test summary 



Rope 
series 



Breaking load 



Diam, 
in 



Mean, 
kips 



SD, 
kips 



SD, 
pet 



Modulus of elasticity 
Mean, SD^ STJ" 
pet 



Breaking stress 



Yield stress 



Torque K 



10 6 psi 



10 6 psi 



Mean 



SD, 



kip/in kip/in 



SD, 
pet 



Mean SD, 
kip/in kip/in 2 



SD, 
pet 



Mean, 
Ibf-ft 
kip 



SD, 
Ibf- 
ft/kip 



SD, 
pet 



A 
B 
C 

D 
E 
F 
G 

H 



1 

1-1/2 
1-1.4 
3/4 
1-7/8 
2 

1-1/4 
1-1/2 



91.14 
208.64 
158.57 

52.09 
331.30 
346.85 
136.91 
207.64 



0.89 
1.31 
.87 
.30 
4.16 
2.53 
1.53 
1.74 



0.97 
.63 
.55 
.57 

1.26 
.73 

1.12 
.84 



9.42 
10.21 
11.30 
11.37 
10.34 

9.00 
12.58 
10.95 



0.44 
1.46 
1.18 

.89 
2.16 
2.08 

.38 
1.40 



4.72 
14.27 
10.46 

7.84 
20.93 
23.12 

3.05 
12.78 



225.74 
235.19 
251.39 
234.85 
233.44 
214.78 
217.04 
234.06 



2.19 
1.43 
1.39 
1.35 
2.95 
1.57 
2.44 
1.98 



0.97 
.61 
.55 
.58 

1.26 
.73 

1.12 
.85 



185.86 
184.44 
211.52 
190.21 
180.35 
163.58 
192.37 
184.02 



2.78 
1.77 
2.17 
2.99 
5.76 
3.07 
1.85 
1.83 



1.50 

.96 

1.03 

1.57 

3.19 

1.88 

.96 

.99 



8.20 
16.45 
14.14 

8.25 
20.18 
14.19 

9.50 
16.54 



0.24 
.13 
.13 
.10 
.50 
.23 
.09 
.11 



2.91 

.81 

.81 

1.20 

2.46 

1.62 

.97 

.69 



SD Standard deviation. 



CONSTRUCTION STRETCH 

Wire rope stretches under load. This stretch comes 
from two sources, elastic and constructional. The elastic 
stretch is reversible, and the rope recovers to its original 
length when the load is removed. The construction stretch 
is not reversible. Construction stretch occurs in new rope 



and happens when a load is first applied. The wires and 
strands are first seated, then act in a constricting manner 
to compress the core permanently. Construction stretch is 
more pronounced in fiber-core ropes than in wire-rope- 
core or strand-core ropes. 

When a tensile test is made on a rope, and the con- 
struction stretch has not been removed, it adds to the 



13 



elongation on the rope during the initial loading. This will 
give an S-shaped stress-strain curve, with sometimes only 
a small central linear portion. An example is shown in 
figure 44. All of the rope A series and part of the rope 
B series were run in this manner, resulting in S-shaped 
curves. 

During the rope B series, it was decided to attempt to 
remove the construction stretch prior to the test. It was 
observed from examining the stress-strain curves that the 
linear portion began after the rope was loaded to about 
20 pet of the breaking strength. Consequently, the ropes 
were loaded to 20 pet of the breaking strength and held 
for 10 min or until they stopped stretching. Then the load 
was removed, and the test was made under normal pro- 
cedures. The results are shown in figure 4B. 

This stress-strain plot does not have an S-curve and is 
linear from the beginning. For comparison, the curves 



240 



200 - 



160 



120 



80 



40 




,J a a a d oc 



Yield, 188 3 kip/irT 
f i Breaking stress, 2373 kip/in 2 

/ Modulus, 7.84* I0 6 psi 



KEY 
Y= 78.44I975*X- 19.60323 



from figures 44 and 4B are plotted together in figure 5. 
All subsequent tests were made following this procedure 
for removing construction stretch. None of the following 
tests showed the S curves. 



BREAKING LOAD VERSUS GAUGE LENGTH 

Breaking load was plotted against gauge length to 
determine the effect of sample length on breaking load 
(fig. 6). The plots show a definite effect of length on 
breaking strength. The shorter samples have higher break- 
ing strengths than the longer samples. There seems to be 
little effect on samples of 15 ft and longer. However, the 
2-ft samples have much higher strength. Even the 5- and 
10-ft samples show higher strength. This is true for the 
3/4-in-diameter samples as well as the 2-in-diameter 
samples. The reason for this phenomenon is not known. 
However, it can be hypothesized that shorter ropes with 
rigidly attached sockets form a more rigid structure in the 
test machine, thus exhibiting higher "system strength." 

BREAKING LOAD VERSUS REEL POSITION 

The samples were cut from the reel in a random order 
to determine whether any variations in properties existed 
along the length of the rope. When the variables were 
plotted against reel position, there was no correlation 
shown between any factor and the position on the reel. 
The most important variable in this respect is the breaking 
strength. Figure 7 shows two plots of breaking strength 
against reel position, for ropes B and D. As can be seen, 
there is no correlation. The results are the same for the 
other samples. 



240 



200- 



160 



i20 



80 



40 





1 1 // 1 LoOODOlOaOCEDI 




B 


/V DDDQ 


- 




A°\ 






Ay Yield, 185 3 kip/in z 
P / Breaking stress, 237.3 kip/in 2 




~~ 


- 


. 


Jl Modulus, 8 63* I0 6 psi 


_ 


- 


// 


- 




f ' KEY 




- 


P/ ■ Y = 86.33028I*X +11.294128 


- 


f 


/ 0.2-pct yield 




ft 






'// 




" 


f/ 




- 


1 


1 1 I i I i 





I 2 3 4 5 6 7 

STRAIN, pet in /in 

Figure 4. -Stress versus strain, rope B. A, 4.81 3-ft sample; 
B, 4.81 8-ft sample. 



240 



200 





I 60 






JC 




<n 


I 20 


in 




id 




rr 




I- 




co 


80 



40 





. 


' *r „ a 




, A / D 


— 


/A A / D 




/a /d 


- 


/* / 




* J 


- 


^ r 




fi / 




f 1 I 


- 


t / 




/ / KEY 

A j ° Test 3, no prestretch 


■ 




' r A Test 16, 40- kip prestretch 




- / / Y| = 78.44*X|- 19.60 


- 


/ r/ --Y ? =86.33*X p+l 1.29 




/ D/ 




/ i i i i i i 


- 



2 3 4 

STRAIN, pet in/in 



Figure 5.-Effect of prestretching on rope samples, rope B. 



14 




2 10 
209 
208 
207 
206 
205 



21 I 



210 



- 209 



- 208 



207 



d 


1 


1 


1 ' 


1 ' 


D 








B 


- 


D 






- 






D 


a 


■ 


D 


D 


a 


D 


D 




1 




1 


a 
l 







1 




1 


1 


D 


52.4 


D 










- 


52.2 


a 


D 


D 


a 




- 


52.0 








D 




- 


51.8 










D 


- 


<^l G 




D 

1 


' 


1 


D 

1 


- 



353 
352 
351 
350 
349 
348 
347 
346 
345 
344 
343 



F _ 

D ~~ 

~ a ~ 

~ a ° " 

-a - 
a 

a 

- o 

D _ 

a 

a 

t i i i 2 , i , : 



6 - 

D 

D _ 

a 

D 

a 



10 20 30 

GAUGE LENGTH, ft 



40 



10 20 30 

GAUGE LENGTH, ft 



40 



Figure 6.-Breaking load versus sample length. A, Rope A; 8, rope B; C, rope C; D, rope D; E, rope E; F, rope F; G, rope H. 



15 



<L 1 1 




i 


1 


1 




D 1 




. A 


□ 








D 


210 


- 












209 






D 








208 

9fY7 


□ 


D 
1 


1 


n 

D D 

1 


a 

1 


a 

D 

1 




50 I 00 I 50 200 250 

POSITION ON REEL, ft 



300 



Figure 7.-Effect of sample position on reel. A, Rope B; B, rope D. 



EFFECTS OF STROKE RATE ON RESULTS 

The "Wire Rope Users Manual" states that for a 
strength test to be valid there must be a "gradually applied 
load that will not exceed a stroke rate of 1 in/min." All of 
the baseline tests to determine physical factors were run 
at a stroke rate of 1 in/min regardless of the size of the 
sample. 

It was desired to see if strain rate had any effect on 
the results. At a stroke rate of 1 in/min, it is obvious that 
the strain rate of a 2-ft sample will be 15 times the strain 
rate of a 30-ft sample. For a 2-ft sample to have the same 
strain rate as a 30-ft sample at a stroke rate of 1 in/min, 
the stroke rate for the 2-ft sample would have to be 
1/15 in/min. For a 30-ft sample to have the same strain 
rate as a 2-ft sample at a stroke rate of 1 in/min, the 
stroke rate for the 30-ft sample would have to be 
15 in/min. To determine the effects of varying strain rates 
on the samples, a series of samples with zinc sockets were 
made up, all of 15 ft in length. The stroke rates tested 
were 0.0625, 0.125, 1, 8, and 16 in/min. These stroke rates 
cover the variations in strain rate discussed above. The 
results are shown in table 11 and in figure 8. Figure &4 
shows that the breaking elongation is lessened as the 
stroke rate is increased. Figure 85 shows that the modulus 
of elasticity is increased slightly as the stroke rate is 
increased. This, of course, correlates with the decreased 
elongation as the stroke rate is increased. As can be seen 
in figure 8C, there is no effect on breaking strength from 
the variation in stroke rate over the ranges shown. The 
correlation coefficient for breaking strength versus stroke 
rate has the value of 0.279, which indicates no correlation 
for this relationship. 



4.4 
4.3 

■£ 4.1 
o 



£ 4.0 

§3.9 

" 3.8 

3.7 

3.6 



u — 


1 


1 ' 1 ' 1 ' 1 


1 1 


1 


- A 


D 






- 


D 






D 


- 


- 


D 






- 


- 




Y = -0. 1 79606 * X + 4.020978 




D 
D 


i 


1 


i 


1 1 


i 




140 



139 



< 



138 



137 - 



2 '36 
m 



135 - 



134 



'_ c 


1 i I 


'l'|i 


1 ' 1 
a 


i 


- 


- a 


D 








- 


- 








□ 


- 


- 




□ 






- 


~~ D 




a 




□ 


_ 


- 










- 




.!_□_< L_ 


i>i, 


i , i 


■ 





-1.4 



-0.6 -0.2 0.2 0.6 
LOG STROKE, in/min 



1.0 



1.4 



Figure 8.-Effect of log stroke rate, rope G. A, Elongation; 
8, modulus; C, breaking load. 



EFFECT OF GAUGE LENGTH ON 
MODULUS OF ELASTICITY 

When the data tables (tables 5-12) are examined, it 
becomes apparent that the columns involving strain 
measurements have high errors compared with the col- 
umns involving load or torque measurements. The modu- 
lus of elasticity, the breaking strain, and the yield strain all 
show these high errors. And yet, when samples of the 
same length are compared, the values are shown to be 
close to each other. Plots of modulus of elasticity, 
breaking strain, and yield strain against gauge length all 
show correlation, although not necessarily linear correla- 
tion. Figure 9 shows plots of modulus of elasticity versus 
gauge length for the various test ropes. These plots show 



16 



10.4 




. 


1 


1 1 1 1 1 1 lo. 


- 


B 


^__^. o - 


- 




nS*^ o 


1 




D / 


~ : 


o/ 


\ 


- 


/d 
la 


Y = 0.l/(7.85005E-03 + 0.233202/X) J 


: 


1 1 


i _ j : 




F 



"i r 



Y = 0.l/(8.4877E-03*0.23029/X) 



J I I L 



50 100 150 200 250 300 350 400 450 

GAUGE LENGTH, in 



50 100 150 200 250 300 350 400 450 500 

GAUGE LENGTH, in 



Figure 9.-Modulus versus gauge length for various ropes. A, Rope A; B, rope B; C, rope C; D, rope D; E. rope E; F, rope F; G, rope H. 



17 



that the modulus of elasticity is lowest for the 2-ft samples 
and highest for the 30- and 35-ft samples, initially in- 
creasing rapidly in value with gauge length, then leveling 
off at the higher gauge lengths. 

The tensile machine does not measure gauge length 
directly. During the initial calibration of the machine, very 
precise measurements were made of the elongation and 
compression of the machine components over the full 
range of load capability. These components included the 
columns, heads, grips, pins, and sockets. The deflection 
data are contained in the data logging program. The pro- 
gram subtracts from the movement of the actuator the 
appropriate deflection at the sensed load for all of the 
involved components. The different grips and sockets for 
each rope size are included individually in the program. 
After pretest stretching, the load is removed, the gauge 
length is measured manually, and the actuator position is 
set to zero. Consequently, a very accurate and repro- 
ducible measurement is made of the change in distance 
between the socket ends during a run, which is nominally 
the gauge length for a solid sample. In the case of a 
socketed wire rope, the wire is not fastened rigidly to the 
socket end. The rope is broomed and cast with epoxy or 
zinc in the cone of the socket. Thus, the compressibility 
of the material in the socket becomes a variable. 

If an assumption is made that the broomed end of the 
rope can stretch and move to some degree out of the 
socket, then an explanation can be made for the high 
errors of the elongation measurements. There is some 
physical justification for this assumption. Markers placed 
on the socket ends with a pointer on the rope showed 
some movement of the rope end out of the socket when a 
load was applied. The rope end moved back into the 
socket when the load was removed. Further, the epoxy 
resin has a very low modulus of compression. Zinc has a 
higher modulus of compression, but it is still much lower 
than that of the high-carbon steel of which the wires are 
made. 

Consider the following. The broomed end in each 
socket moves out of the socket by an amount proportional 
to the load. Because the tensile machine measures the 
distance between the socket ends, it determines the sum of 
the lengths that each broom pulls out plus the elongation 
of the original length of rope measured between the 
sockets (the gauge length). The amounts that the 
broomed ends move out are independent of the gauge 
length of the sample. Consequently, the percentage error 
becomes less as the gauge length increases. 

It is possible to calculate this error if elongation at a 
constant load is plotted against gauge length for different 
sample lengths. For a solid rod, elongation would be 
directly proportional to gauge length within the elastic 
range. For a wire rope, elongation should still be directly 
proportional to gauge length, but with an intercept on the 
y-axis (elongation). The intercept represents the error 
caused by the broom pullout. This error is directly 
proportional to load while within the elastic region of the 
stress-strain plot. 



The values for elongation at a constant load cannot be 
taken directly from the data tables. If the B plots in fig- 
ures 2 and 3 are examined, it can be seen that the slopes 
for the stress-strain curves do not go through the origin of 
the coordinates, because of the preload put on the sample 
and the subsequent zeroing of the stroke. This can be al- 
lowed for by taking the slope of each stress-strain plot and 
mathematically forcing it through the origin. The slope of 
the stress-strain curve is the modulus of elasticity and is 
given in column 2 of the data tables (tables 5-11). 

Then, 



modulus = stress/strain, 

strain = stress/modulus, 

strain = elongation/gauge, 

and elongation = strain x gauge. 



(1) 
(2) 
(3) 
(4) 



Thus, it is possible to calculate elongation at a given 
strain, knowing the modulus of elasticity. These calcu- 
lations are shown for a given stress of 100,000 psi in 
tables 14-20. The given stress of 100,000 psi is approxi- 
mately at the midpoint of the elastic region of the stress- 
strain plot. As is demonstrated in the tables, strain is 
calculated from the modulus and the given stress using 
equation 2. Then, elongation is calculated from the strain 
and gauge using equation 4. 

Table 1 4.-Effect of sample length on modulus and 
elongation at 100,000-psi stress for rope A 



Sample 


Mod 


ulus of elasticity, 


10 6 psi 


Strain, 




length, 




Calcu- 


Differ- 


Differ- 


Elonga- 


ft 


Actual 


lated 


ence 


ence, 
squared 


in/in 


tion, in 


4.90 .. . 


8.26 


8.257 


-0.003 


0.00001 


0.01211 


0.712 


5.01 . . . 


8.48 


8.293 


-.187 


.0349 


.01179 


.709 


10.00 . . 


9.50 


9.195 


-.305 


.0931 


.01053 


1.263 


10.13 . . 


8.89 


9.208 


.318 


.1010 


.01125 


1.367 


14.96 . . 


9.43 


9.540 


.110 


.0122 


.01060 


1.904 


15.14 . . 


9.89 


9.549 


-.341 


.1164 


.01011 


1.837 


15.21 . . 


9.49 


9.552 


.062 


.0039 


.01054 


1.923 


20.00 . . 


9.57 


9.726 


.156 


.0243 


.01045 


2.508 


20.03 . . 


9.77 


9.727 


-.043 


.0019 


.01024 


2.460 


20.27 . . 


9.59 


9.733 


.143 


.0205 


.01043 


2.536 


35.08 . . 


10.22 


9.973 


-.247 


.0608 


.00978 


4.119 


35.21 . . 


9.87 


9.975 


.105 


.0109 


.01013 


4.281 


35.32 . . 


9.90 


9.976 


.076 


.0057 


.01010 


4.281 


Mean . 


9.45 


NAp 


NAp 


NAp 


NAp 


NAp 


SS ... 


NAp 


NAp 


NAp 


.4856 


NAp 


NAp 


Variatio 


n NAp 


NAp 


NAp 


.0405 


NAp 


NAp 


SD ... 


.58 


NAp 


NAp 


.2012 


NAp 


NAp 


SD.. 














pet . 


6.09 


NAp 


NAp 


2.1286 


NAp 


NAp 


NAp N 


ot applicable. 










SD S 


tandard deviation. 










SS S 


urn of squares. 










NOTE.-fv 


lodulus of 


elasticity 


= 0.1/(9.68819E-03 


+ 0.142489/X). 



18 



Table 15.-Effect of sample length on modulus and 
elongation at 100,000-psi stress for rope B 



Table 17.-Effect of sample length on modulus and 
elongation at 100,000-psi stress for rope D 



Sample 


Modulus of elasticity, 10 6 psi 


Strain, 


Elonga- 


Sample 
length, 


Modulus of elasticity, 


10 6 psi 


Strain, 




length, 




Calcu- 


Differ- 


Differ- 




Calcu- 


Differ- 


Differ- 


Elonga- 


ft 


Actual 


lated 


ence 


ence, 
squared 


in/in 


tion, in 


ft 


Actual 


lated 


ence 


ence, 
squared 


in/in 


tion, in 


4.81 . . . 


7.84 


8.410 


0.570 


0.3252 


0.01276 


0.736 


1.88 .. . 


9.22 


8.595 


-0.625 


0.3910 


0.01085 


0.245 


4.82 . . . 


8.90 


8.416 


-.484 


.2341 


.01124 


.650 


4.85 .. . 


10.82 


10.652 


-.168 


.0284 


.00924 


.538 


4.82 . . . 


8.63 


8.416 


-.214 


.0457 


.01159 


.670 


4.86 .. . 


. 10.82 


10.655 


-.165 


.0272 


.00924 


.539 


5.06 .. . 


8.11 


8.554 


.444 


.1970 


.01233 


.749 


4.91 . . . 


10.75 


10.671 


-.079 


.0062 


.00930 


.548 


9.64 .. . 


10.51 


10.136 


-.374 


.1400 


.00951 


1.101 


5.09 .. . 


10.98 


10.728 


-.252 


.0634 


.00911 


.556 


10.02 . . 


10.35 


10.215 


-.135 


.0182 


.00966 


1.162 


9.81 . . . 


11.45 


11.535 


.085 


.0073 


.00873 


1.028 


14.64 . . 


10.95 


10.896 


-.054 


.0029 


.00913 


1.604 


9.93 . . . 


11.41 


11.546 


.136 


.0186 


.00876 


1.044 


14.71 . . 


11.00 


10.904 


-.096 


.0093 


.00909 


1.605 


15.01 . . 


11.84 


11.869 


.029 


.0008 


.00845 


1.521 


19.60 . . 


11.04 


11.310 


.270 


.0730 


.00906 


2.130 


15.02 . . 


11.77 


11.869 


.099 


.0098 


.00850 


1.531 


20.17 . . 


11.33 


11.346 


.016 


.0003 


.00883 


2.136 


19.96 . . 


11.89 


12.031 


.141 


.0200 


.00841 


2.014 


34.88 . . 


11.76 


11.895 


.135 


.0181 


.00850 


3.559 


20.00 . . 


11.77 


12.032 


.262 


.0688 


.00850 


2.039 


35.00 . . 


12.07 


11.897 


-.173 


.0298 


.00829 


3.480 


20.07 . . 


12.19 


12.034 


-.156 


.0243 


.00820 


1.976 


Mean . 


10.21 


NAp 


NAp 


NAp 


NAp 


NAp 


20.09 . . 


11.86 


12.035 


.175 


.0305 


.00843 


2.033 


SS . . . 


NAp 


NAp 


NAp 


1.0936 


NAp 


NAp 


29.88 . . 


12.43 


12.200 


-.230 


.0530 


.00805 


2.885 


Variatio 


n NAp 


NAp 


NAp 


.0994 


NAp 


NAp 


29.93 . . 


12.40 


12.200 


-.200 


.0399 


.00806 


2.896 


SD. . . 


1.46 


NAp 


NAp 


.3153 


NAp 


NAp 


30.16 . . 


12.02 


12.203 


.183 


.0335 


.00832 


3.011 


SD.. 














Mean . 


11.48 


NAp 


NAp 


NAp 


NAp 


NAp 














SS .. . 


NAp 


NAp 


NAp 


.8226 


NAp 


NAp 


pet . . 


14.27 


NAp 


NAp 


3.0889 


NAp 


NAp 


Variation NAp 


NAp 


NAp 


.0548 


NAp 


NAp 


NAp N 


ot applicable. 










SD ... 


.81 


NAp 


NAp 


.2342 


NAp 


NAp 


SD S 


tandard deviation. 
























SS S 


urn of squares. 










SD .. 




























pet . . 


7.09 


NAp 


NAp 


2.0406 


NAp 


NAp 


NOTE.-K 


lodulus of elasticity = 


= 0.1/(9.68819E-03 


+ 0.142489/X). 


NAo N 


ot applicab 


e. 











Table 16.-Effect of sample length on modulus and 
elongation at 100,000-psi stress for rope C 



SD Standard deviation. 
SS Sum of squares. 

NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). 



Sample 


Modulus of elasticity, 10 6 psi 






Table 18.-Effect of sample length on modulus and 


length, 




Calcu- 


Differ- 


Differ- 


Strain, 


Elonga- 




elongation at 100,000-psi 


stress for 


rope E 




ft 




lated 






in/in 


























squared 




Sample 
length, 


Modulus of elasticity, 


10 6 psi 


Strain, 




4.76 . . . 


9.34 


9.002 


-0.338 


0.1143 


0.01071 


0.612 




Calcu- 


Differ- 


Differ- 


Elonga- 


4.84 . . . 


8.61 


9.049 


.439 


.1929 


.01161 


.675 


ft 


Actual 


lated 


ence 


ence, 


in/in 


tion, in 


4.98 .. . 


9.65 
10.70 


9.129 
10.727 


-.521 
.027 


.2710 
.0007 


.01036 
.00935 


.619 
1.087 










squared 






9.69 . . . 


1.96 .. . 


6.34 


6.219 


-0.121 


0.0146 


0.01577 


0.371 


9.98 .. . 


10.94 


10.785 


-.155 


.0239 


.00914 


1.095 


2.00 .. . 


6.83 


6.287 


-.543 


.2945 


.01464 


.351 


14.98 . . 


11.74 


11.477 


-.263 


.0690 


.00852 


1.531 


4.88 . . . 


9.25 


9.199 


-.051 


.0026 


.01081 


.633 


19.80 . . 


11.97 


11.847 


-.123 


.0152 


.00835 


1.985 


4.91 . . . 


9.72 


9.217 


-.503 


.2529 


.01029 


.606 


19.94 . . 


11.02 


11.855 


.835 


.6973 


.00907 


2.171 


9.87 . . . 


10.76 


10.985 


.225 


.0506 


.00929 


1.101 


19.98 . . 


11.95 


11.857 


-.093 


.0086 


.00837 


2.006 


9.93 . . . 


10.49 


10.998 


.508 


.2577 


.00953 


1.136 


34.81 . . 


12.26 


12.381 


.121 


.0146 


.00816 


3.407 


14.90 . . 


10.99 


11.737 


.747 


.5586 


.00910 


1.627 


34.83 . . 


12.25 


12.381 


.131 


.0172 


.00816 


3.412 


14.97 . . 


11.77 


11.745 


-.025 


.0006 


.00850 


1.526 


34.95 . . 


12.36 


12.384 


.024 


.0006 


.00809 


3.393 


19.82 . . 


12.62 


12.142 


-.478 


.2281 


.00792 


1.885 


35.07 . . 


12.64 


12.386 


-.254 


.0645 


.00791 


3.329 


20.01 . . 


12.34 


12.155 


-.185 


.0344 


.00810 


1.946 


35.36 . . 


12.49 


12.392 


-.098 


.0096 


.00801 


3.397 


29.85 . . 


12.57 


12.584 


.014 


.0002 


.00796 


2.850 


35.39 . . 


12.48 


12.393 


-.087 


.0076 


.00801 


3.403 


29.96 . . 


12.59 


12.588 


-.002 


5E-06 


.00794 


2.856 


Mean . 


11.36 


NAp 


NAp 


NAp 


NAp 


NAp 


Mean . 


10.52 


NAp 


NAp 


NAp 


NAp 


NAp 


SS .. . 


NAp 


NAp 


NAp 


1.5069 


NAp 


NAp 


SS .. . 


NAp 


NAp 


NAp 


1.6948 


NAp 


NAp 


Variatio 


n NAp 


NAp 


NAp 


.1076 


NAp 


NAp 


Variatio 


n NAp 


NAp 


NAp 


.1541 


NAp 


NAp 


SD. .. 


1.28 


NAp 


NAp 


.3281 


NAp 


NAp 


SD . .. 


2.16 


NAp 


NAp 


.3925 


NAp 


NAp 


SD.. 
pet . . 


11.27 


NAp 


NAp 


2.8880 


NAp 


NAp 


SD .. 
pet . . 


20.54 


NAp 


NAp 


3.7303 


NAp 


NAp 


NAp N 


ot applicable. 










NAp N 


ot applicable. 










SD S 


tandard deviation. 










SD S 


tandard deviation. 










SS S 


jm of squares. 










SS S 


jm of squares. 











NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). 



NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). 



19 



Table 19.-Effect of sample length on modulus and 
elongation at 100,000-psl stress for rope F 



Sample 


Modulus of elasticity, 10 6 psi 


Strain, 




length, 




Calcu- 


Differ- 


Differ- 


Elonga- 


ft 


Actual 


lated 


ence 


ence, 
squared 


in/in 


tion, in 


1.94 .. . 


5.66 


5.441 


-0.219 


0.0481 


0.01767 


0.411 


2.17 . . . 


5.93 


5.770 


-.160 


.0256 


.01686 


.439 


2.18 . . . 


5.17 


5.783 


.613 


.3763 


.01934 


.506 


5.20 .. . 


8.46 


8.211 


-.249 


.0618 


.01182 


.738 


5.38 .. . 


9.34 


8.295 


-1.045 


.0910 


.01071 


.691 


9.91 . . . 


10.04 


9.593 


-.447 


.1998 


.00996 


1.184 


10.18 . . 


8.81 


9.641 


.831 


.6898 


.01135 


1.387 


10.27 . . 


9.15 


9.656 


.506 


.2560 


.01093 


1.347 


14.80 . . 


10.89 


10.220 


-.670 


.4484 


.00918 


1.631 


14.92 . . 


10.31 


10.231 


-.079 


.0062 


.00970 


1.737 


15.34 . . 


10.03 


10.268 


.238 


.0568 


.00997 


1.835 


19.94 . . 


10.41 


10.582 


.172 


.0295 


.00961 


2.299 


20.28 . . 


10.52 


12.600 


.080 


.0064 


.00951 


2.313 


30.13 . . 


10.81 


12.959 


.149 


.0223 


.00925 


3.345 


30.23 . . 


11.21 


12.962 


-.248 


.0616 


.00892 


3.236 


Mean . 


9.12 


NAp 


NAp 


NAp 


NAp 


NAp 


SS . . . 


NAp 


NAp 


NAp 


3.3796 


NAp 


NAp 


Variatio 


n NAp 


NAp 


NAp 


.2414 


NAp 


NAp 


SD... 


1.99 


NAp 


NAp 


.4913 


NAp 


NAp 


SD .. 














pet . . 


21.82 


NAp 


NAp 


5.3897 


NAp 


NAp 



NAp Not applicable. 
SD Standard deviation. 
SS Sum of squares. 

NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). 

Table 20.-Effect of sample length on modulus and 
elongation at 100,000-psi stress for rope H 



Sample 


Modulus of elasticity, 10 6 psi 


Strain, 




length, 




Calcu- 


Differ- 


Differ- 


Elonga- 


ft 


Actual 


lated 


ence 


ence, 
squared 


in/in 


tion, in 


2.06 .. . 


6.12 


5.787 


-0.333 


0.1106 


0.01634 


0.404 


2.06 .. . 


5.15 


5.787 


.637 


.4062 


.01942 


.480 


5.06 .. . 


8.55 


8.638 


.088 


.0077 


.01170 


.710 


5.08 .. . 


8.59 


8.649 


.059 


.0035 


.01164 


.710 


10.10 . . 


10.38 


10.391 


.011 


.0001 


.00963 


1.168 


10.11 . . 


10.90 


10.394 


-.506 


.2564 


.00917 


1.113 


20.12 . . 


11.30 


11.566 


.266 


.0705 


.00885 


2.137 


20.15 . . 


11.89 


11.568 


-.322 


.1040 


.00841 


2.034 


30.16 . . 


11.90 


12.021 


.121 


.0147 


.00840 


3.041 


30.21 . . 


12.07 


12.023 


-.047 


.0022 


.00829 


3.003 


Mean . 


9.69 


NAp 


NAp 


NAp 


NAp 


NAp 


SS ... 


NAp 


NAp 


NAp 


.9761 


NAp 


NAp 


Variatio 


n NAp 


NAp 


NAp 


.1085 


NAp 


NAp 


SD... 


2.49 


NAp 


NAp 


.3293 


NAp 


NAp 


SD.. 














pet . . 


25.71 


NAp 


NAp 


3.4004 


NAp 


NAp 


NAp N 


ot applicable. 










SD S 


landard deviation. 










SS S 


jm of squares. 










NOTE.-N 


lodulus of elasticity = 


= 0.1/(9.68819E-03 


+ 0.142489/X). 



Plots of elongation versus gauge for the test ropes are 
shown in figure 10. As predicted, elongation is a linear 
function of gauge length with an intercept off the origin. 
The intercept is the sum of the amounts of the pullout of 
each broomed end at a stress of 100,000 psi. In plot A, 



which shows a plot for the rope A series samples, the 
equation of the slope is given as 

Y = 9.68819E-03 * X + 0.142489, (5) 

where Y = elongation, in, 

and X = gauge length, in. 

If the elongation (Y) is divided by the gauge length (X), 
the strain (S) is calculated as per equation 3. 
Equation 5 becomes 



where 



S = 9.68819E-03 + 0.142489/X, (6) 

S = strain, in/in. 



If the stress is divided by the strain (S), the modulus 
of elasticity (Mod) is calculated as per equation 1. Equa- 
tion 6 becomes 

Mod = 100,000/(9.68819E-03 + 0.142489/X), (7) 

where Mod = modulus of elasticity, psi. 

If equation 7 is divided by 1,000,000, the modulus of 
elasticity is converted from pounds per square inch to mil- 
lion pounds per square inch. Equation 7 then becomes 



Mod = 0.1/(9.68819E-03 + 0.142489/X). 



(8) 



Plots of modulus of elasticity in million pounds per 
square inch versus gauge length in inches are given in fig- 
ure 9 for all of the baseline test series. Also shown in the 
plots are the equations for the modulus of elasticity devel- 
oped as in equation 8. The curves shown were not deter- 
mined by curve fitting. These curves are derived from the 
elongation data for each series of tests and calculated as 
shown above in equations 5 through 8. 

The linearity of the elongation-versus-gauge-length plots 
and the positive intercepts prove the hypothesis that there 
is a constant error in elongation measurement that is pro- 
portional to load and independent of gauge length. r . r he fit 
of the data points to the calculated equations for modulus 
of elasticity on figure 9 is further proof of the hypothesis. 

The modulus of elasticity for rope A can be calculated 
using equation 8 and the gauge length data shown in ta- 
ble 14. The calculated values can be compared with the 
experimental values. The standard deviation for regression 
of the experimental data about the calculated curve is 
shown at the bottom of column 5 of table 14. This is 
much lower than the standard deviation for the experi- 
mental data (column 2), without considering the effects of 
gauge length. The same is true for the other series (tables 
15-20). 

One way to determine strain accurately would be to 
mechanically mount an elongation measuring device such 
as the one developed by Versuchsgrube Tremonia (3). 
This procedure is generally undesirable because it would 



20 



Y = 7.96601 E- 03 *X* 0.082774 

J I I I I I 




1 

1 F 


i i i i i \<y i 


- 


- 


/d 


_ 


~ r/ 


Y = 8.487665E - 03 *X ♦ 0.230287 

i i i i i i i 


- 



Y = 766I7 35E-03*X + 0.23774 

' I I 1 -1 L 



100 150 200 250 300 350 400 450 

GAUGE LENGTH, in 



100 150 200 250 300 350 400 450 

GAUGE LENGTH, in 



Figure 10.-Elongation versus gauge length at 100,000-psi stress for various ropes. A, Rope A; B, rope B; C, rope C; D, rope D; 
E, rope E; F, rope F; G, rope H. 



21 



be necessary to stop the test before yield is reached, re- 
move the load, open the protection boxes, dismount the 
device, close the boxes, then reload. All these steps would 
be time consuming and could affect the later test results. 
Other possibilities would be to develop a precise optical 
ranging system or a system with disposable components. 
The elongation corrections at a stress of 100,000 psi are 
shown in table 21 for all of the rope series tested. Also 
shown in the table are the rope diameters, the rope cross- 
sectional metallic areas, and the loads on the ropes at 
100,000 psi stress. In figure 11, the elongation correction 
in inches is plotted against the load in kips. The load in 
kips was calculated from the rope metallic area and the 
stress of 100,000 psi. The plot shows that the elongation 
correction is essentially constant for the ropes from 1-1/4- 
to 2-in diameter. Further, a straight line covers the ropes 
from 3/4- to 1-1/4-in diameter. However, considerably 
more work would have to be done before any real 
correlation could be proven. It appears likely that the 
elongation correction for each rope diameter and con- 
struction would have to be done by testing. The elonga- 
tion correction factor could then be placed in the com- 
puter program, and the effects of varying gauge length 
would be eliminated. 

Table 21. -Elongation correction versus 
rope diameter at 100,000-psi stress 



Diam, 
in 



Area, 
in 2 



Load, 
kips 



Correction, 
in 



Sample 



3/4 . 

1 . . . 
1-1/4 
1-1/2 
1-1/2 
1-7/8 

2 . . . 



0.222 


22.2 


0.083 


.404 


40.4 


.143 


.631 


63.1 


.201 


.887 


88.7 


.233 


.887 


88.7 


.238 


1.419 


141.9 


.205 


1.615 


161.5 


.230 



D 
A 
C 
B 

H 

E 

F 



0.26 



.22 - 



18 - 



o 

UJ 

k .14 

o 

o 



10 - 

D 



.06 



"i r 



I 00-kip/in 2 stress level 



J_ 



_!_ 



20 40 60 80 1 00 I 20 1 40 1 60 

LOAD, kips 



COMPARISON OF ZINC AND EPOXY SOCKETING 

The modulus of elasticity for epoxy is approximately 
500,000 psi, while that for zinc is about 12,000,000 psi. 
The question was whether zinc-socketed ropes would be- 
have differently than epoxy-resin-socketed ropes. It must 
be remembered that the material in the socket is not epoxy 
or zinc alone but a composite of high-carbon steel wires 
plus a zinc or an epoxy fdler. 

A set of 10 ropes was made with zinc-socketed ends. 
The lengths were 2, 5, 10, 20, and 30 ft, with two samples 
each. The rope used for the tests was the same 1-1/2-in- 
diameter rope that was used for the rope B series so that 
the results could be compared directly. The data for the 
zinc series are shown in table 12. These data can be 
compared with the rope B series shown in table 6. The 
results are remarkably similar. The breaking strength ver- 
sus gauge length is shown in figure 12. The plot shows no 



21 I 



210 



209 - 



o' 208 

< 

o 



207 



206 



205 



a ' 


1 ' 1 


1 1 


1 1 ' 1 


1 1 ' 1 


1 


_o 










- 


a 










- 


- 


D 








- 






D 


B 






□ 


Ob 


a 


D 




a 












D 


- 


KEY 






A 


- 


- 


n Epoxy 
a Zinc 




A 




- 


' 


i , i 


i 


1 , 1 


1 , 1 


i 



12 



16 20 24 

GAUGE LENGTH, ft 



28 



32 



36 




Epoxy: Y,= 7.85005E-03»X, + 0.233202 
-■* Zinc: Y 2 = 7.661 735E-03»X 2 + 0.23774 



50 100 150 200 250 300 350 400 450 
GAUGE LENGTH, in 



Figure 1 1 -Elongation correction for stretch of socket filler 
versus load. 



Figure 12.- Breaking strength and elongation versus gauge 
length for epoxy and zinc terminations. 



22 



significant difference between the zinc and epoxy termina- 
tions. This is verified by the means and standard devia- 
tions in tables 6 and 12. A plot of elongation versus gauge 
length for both series is also shown in figure 12. Neither 
the correction factors nor the slopes in the plots of 
elongation versus gauge length are statistically different. 
Finally, plots of modulus versus gauge length for both zinc 
and epoxy resin are shown in figure 13. Again, the data 
points and the independently determined equations for the 
modulus as a function of gauge length are very close to 
each other. The conclusion is that there is no significant 
difference in the behavior of the zinc and the epoxy resin 
socketed ropes for breaking strength tests. Both the zinc 
sockets and the epoxy resin sockets developed 100 pet of 
the normal breaking strength of the ropes. During the 
testing for all of the rope series, the resin-socketed 
terminations developed 100 pet of the normal breaking 
strength of the ropes. 

The U.S. Code of Federal Regulations (7) states that 
for wire rope load end attachments 

(a) Wire rope shall be attached to the load by a 
method that develops at least 80 pet of the nominal 
strength of the rope. 

(b) Except for terminations where use of other 
materials is a design feature, zinc (spelter) shall be 
used for socketing wire ropes. 

The wording in the regulations is identical for metal and 
nonmetal open pit mines; sand, gravel, and crushed stone 
operations; metal and nonmetal underground mines; 
underground coal mines; surface coal mines; and surface 
work areas of underground coal mines. 

In Great Britain, the Safety in Mines Research Es- 
tablishment, after extensive testing, found that resin 



sockets were as strong as the rope and has accepted them 
for use in mining (4). The findings in this report agree, 
which suggests that the CFR could be amended to allow 
the use of resin for the socketing of mine ropes. 

TORQUE CALCULATIONS 

The torque on the rope is measured directly by the ten- 
sile machine sensor as a function of time and is reported 
in kip-inches. This value is changed to pound (force) feet 
and reported in the data tables. Examples are shown in 
tables 2 and 3. Plots of torque in pound (force) feet ver- 
sus load in kips are shown in plot C of figures 2 and 3. 
The plots show the data to be linear well into the plastic 
region of the rope. The slope of the plot is called the 
Torque K, and has the units pound (force) feet per kip. 
If the Torque K is known for a rope, it is possible to 
calculate the torque on the rope for virtually any load. 
The Torque K's for all of the rope series are shown in 
tables 5 through 12. A summary of the mean values and 
the standard deviations is shown in table 13. 

A general equation for determining the approximate 
torque in ropes under load was developed by Gibson (5). 
This equation was developed for six-strand ropes with fiber 
cores. He found that the torque was directly proportional 
to the load and the square of the rope diameter and 
indirectly proportional to the lay length. His equation is 
given as 



T = A(D 2 )S/L, 
where T = torque, Ibf-in, 

D = rope diameter, in, 
S = load, lb, 



(9) 



» 10 

Q. 
J 

o 

CO 



10 



_ 


1 1 1 1 1 1 1 1 


- 


A ^B^^ 


- 


- 


*f 


- 


- 


0/ 


- 


- 


fa 


- 


- / 


KEY 


- 


- / 


— o Epoxy: Y| = 0.l/(7.85005E-03 + 0.233202/X!) 


- 


(A 


— * Zinc: Y 2 = 0.1/ (7.66 l735E-03 + 0.23774/X 2 ) 


- 


"1 


i i i i i i i i 


" 



50 100 150 200 250 300 350 400 450 
GAUGE LENGTH, in 

Figure 13.- Modulus versus gauge length for epoxy and zinc 
terminations. 



L = lay length, in, 

and A = 0.91 for Lang lay and 0.55 for regular lay 
ropes. 

The constant A used by Gibson in equation 9 can be 
calculated from the experimental data in table 12, using 
the following equation: 



A = 12KL/1,000D 2 , 
where K = Torque K, lbf-ft/kip. 



(10) 



The results of the calculations of the constant A are 
shown in table 22. Two additional ropes are shown in this 
table, Y and R, which refer to used mine hoist ropes. 
They were added for comparison purposes. The values for 
Gibson's constant A indicate that Gibson's approximations 
are very close to the experimental data as determined on 
the tensile machine. 



23 



Table 22.-Calculation of Gibson's torque constant 



Diam, in 



Rope 1 



Lay, in 



Torque K, 
Ibf-ft/kip 



Gibson 
constant 



Right Lang lay: 

3/4 

1-1/4 

1-1/2 

1-7/8 

Right regular lay: 

1 

1-1/4 

2 

'See table 2 for description. 

2 Mine hoist rope, 6 x 27 flattened strand. 

3 Mine hoist rope, 6 x 30 flattened strand. 



D 
C 
B 

H 
E 
Y 2 
R 3 

A 
G 

F 



5.25 
8.00 
10.00 
10.00 
12.75 
14.50 
12.00 

6.00 

8.07 

13.13 



8.25 
14.14 
16.45 
16.54 
20.18 
17.43 
19.35 

8.20 

9.50 

14.19 



0.915 
.869 
.877 
.882 
.878 
.863 
.793 

.590 
.589 
.559 



SUMMARY 



The operating characteristics of the tensile machine 
have been learned using a variety of rope samples. The 
machine has been determined to have high precision in the 
measurements of load, stroke, and torque. 

All of the rope samples tested were shown to have 
uniform properties along the length of the reel. The 
stroke rate had no effect on either the breaking strength 
of the ropes or on the torque developed as the load 
increased. However, there was slight lessening of the 
breaking elongation at the higher stroke rates. There was 



no difference in the properties of the ropes when either 
zinc or epoxy resin was used as socketing material. The 
elongation of the ropes calculated from the stroke mea- 
surements was shown to vary with the length of the sam- 
ples. This variation was caused by an unaccounted-for 
extrusion of the socketing material. This extrusion can be 
corrected in the computer program, but a series of tests 
would have to be run to determine the additional cor- 
rection factor for each rope size and construction. 



REFERENCES 



1. U.S. Code of Federal Regulations. Title 30-Mineral Resources; 
Chapter I-Mine Health and Safety Administration, Department of 
Labor, Subchapter N-Metal and Nonmetal Mine Safety and Health; 
Part 56, Subpart R, and Part 57, Subpart R Subchapter O-Coal Mine 
Safety and Health; Part 75, Subpart O, and Part 77, Subpart O; 
July 1, 1989. 

2. Committee of Wire Rope Producers. Wire Rope Users Manual. 
AISI, 2d ed., 1981, p. 77. 



3. Versuchsgrube Tremonia (Dortmund, Federal Republic of 
Germany). (Research and Testing in 1985.) Item 3.2.1, 1985, p. 51. 

4. Dodd, J. M. Resin as a Socketing Medium. Wire Ind., v. 48, 
No. 569, May 1981, pp. 343-344. 

5. Gibson, P. T. Wire Rope Behavior in Tension and Bending. 
Paper in Proceedings, First Annual Wire Rope Symposium. WA State 
Univ., Pullman, WA, 1980, pp. 3-31. 



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